Harmonic Analysis Method Based on Power Balance

Abstract:

Nonlinear differential equations are sometimes found by using harmonic balance principle. If it is based on the complex power balance theory, some much more correct and rational results can be obtained. Non-autonomous circuits sometimes include two components, the forced and the self-excited oscillation, they must satisfy respectively the balancing condition of complex power. When we study the nonautonomous circuit, two notable questions should be considered. On the one hand ,the existence of self-excited oscillation of the circuit which contains the dissipative elements depends on whether or not active power can maintain balance. The existence is closely related to the amplitude of excited current source. When the current source is strong enough, the original self-excited oscillation will thus disappear, leaving only a forced component. On the other hand, the existence of the self-oscillation of the lossless circuit which does not contain the dissipative elements is independent from the current amplitude of the excited source. The forced and self-excited oscillation components can simultaneously coexist unconditionally. chaos can easy be produced by the nonlinear coupling of the two harmonic components. The intrinsic attributes of the chaos can be sufficiently revealed with the help of this kind of lossless circuits.

• Periodical: Applied Mechanics and Materials (Volumes 325-326)
• Pages: 1508-1514
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.325-326.1508
• Online since: June 2013
• Authors: Bing Hua Huang, Guang Song Yang, Ya Fen Wei, Ying Huang
• Keywords: Chaos, Harmonic Solution, Non-Autonomous Circuit, Power Balance, Self-Oscillation

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[12] Mathematica Programs:(These are listed in the order of appearance): ①Program-first.nb ②Program-Tab1.nb③Program-Leq.nb④Program-onlyup.nb⑤Program-wh.nb⑥Program-first2.nb⑦Program-Tab2.nb.

DOI: 10.2172/4317513